T he radian is a unit of measure for angles. One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle. The radian is a unit of measure for angles used mainly in trigonometry. It is used instead of degrees. As seen in the figure below, a radian is defined by an arc of a circle. The length of the arc is equal to the radius of the circle. Because of this the radian is a fixed size no matter what the size of the circle is. For reasons that have to do with calculus, the further you go with mathematics the more sense it makes to measure angles not in degrees but in radians. There are `2 pi` radians in a full circle.
Trigonometry, as the name might suggest, is all about triangles. More specifically, trigonometry is about right-angled triangles, where one of the internal angles is 90°. The prime application of trigonometry in past cultures, not just ancient Greek, is to astronomy. The Babylonians were using degree measurement for angles. The Babylonian numerals were based on the number 60, so it may be conjectured that they took the unit measure to be what we call 60°, then divided that into 60 degrees. Today, trigonometry is introduced to students as a method for finding the missing parts of right triangles. The study of trigonometry involves learning how trigonometric functions – such as the sine or cosine of an angle, for example – can be used to work out the angles and dimensions of a particular shape. In this form it is used by surveyors, architects and engineers, as well as navigators and astronomers. So, it is pretty important.